LMFDB - Embedded newform 1.98.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1,98,Mod(1,1)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1, base_ring=CyclotomicField(1))

chi = DirichletCharacter(H, H._module([]))

N = Newforms(chi, 98, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1.1");

S:= CuspForms(chi, 98);

N := Newforms(S);

Level:	$ N $	$=$	$ 1 $
Weight:	$ k $	$=$	$ 98 $
Character orbit:	$[\chi]$	$=$	1.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$59.5852992940$
Analytic rank:	$1$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} + \cdots - 60\!\cdots\!00 $ x^7 - x^6 - 276087571804405990752665088x^5 - 120083887007184048105302098667336699968x^4 + 19373155893793813105741918625198082602849023860244480x^3 + 17598423525325549028964286424215233146805218189713573416303513600x^2 - 58411389055962077878580852277509525104521481793026738328029906710656876544000*x - 6001611580367435872109665775701806052295874267155389813520177925124906158334928977920000
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	multiple of $ 2^{83}\cdot 3^{30}\cdot 5^{10}\cdot 7^{8}\cdot 11^{2}\cdot 19 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.21138e13$ of defining polynomial
Character	$\chi$	$=$	1.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.83847e14 q^{2} -6.70202e22 q^{3} +1.82421e29 q^{4} +3.35065e33 q^{5} +3.91296e37 q^{6} +6.90378e40 q^{7} -1.39919e43 q^{8} -1.45964e46 q^{9} +O(q^{10})$	\(q-5.83847e14 q^{2} -6.70202e22 q^{3} +1.82421e29 q^{4} +3.35065e33 q^{5} +3.91296e37 q^{6} +6.90378e40 q^{7} -1.39919e43 q^{8} -1.45964e46 q^{9} -1.95627e48 q^{10} -7.70331e49 q^{11} -1.22259e52 q^{12} +2.16354e53 q^{13} -4.03075e55 q^{14} -2.24561e56 q^{15} -2.07367e58 q^{16} -6.79786e59 q^{17} +8.52204e60 q^{18} +6.40476e61 q^{19} +6.11230e62 q^{20} -4.62693e63 q^{21} +4.49756e64 q^{22} +8.09777e65 q^{23} +9.37741e65 q^{24} -5.18820e67 q^{25} -1.26318e68 q^{26} +2.25754e69 q^{27} +1.25940e70 q^{28} +4.54709e70 q^{29} +1.31110e71 q^{30} +3.94871e72 q^{31} +1.43242e73 q^{32} +5.16277e72 q^{33} +3.96891e74 q^{34} +2.31322e74 q^{35} -2.66269e75 q^{36} -1.34752e76 q^{37} -3.73940e76 q^{38} -1.45001e76 q^{39} -4.68820e76 q^{40} -1.03033e77 q^{41} +2.70142e78 q^{42} +3.26343e79 q^{43} -1.40525e79 q^{44} -4.89073e79 q^{45} -4.72786e80 q^{46} -1.05368e81 q^{47} +1.38978e81 q^{48} -4.66374e81 q^{49} +3.02912e82 q^{50} +4.55594e82 q^{51} +3.94675e82 q^{52} -3.91708e83 q^{53} -1.31806e84 q^{54} -2.58111e83 q^{55} -9.65971e83 q^{56} -4.29248e84 q^{57} -2.65481e85 q^{58} +8.07111e85 q^{59} -4.09648e85 q^{60} -4.86128e86 q^{61} -2.30544e87 q^{62} -1.00770e87 q^{63} -5.07726e87 q^{64} +7.24926e86 q^{65} -3.01427e87 q^{66} -6.80563e87 q^{67} -1.24008e89 q^{68} -5.42714e88 q^{69} -1.35057e89 q^{70} -4.42259e89 q^{71} +2.04231e89 q^{72} +2.87024e90 q^{73} +7.86743e90 q^{74} +3.47714e90 q^{75} +1.16837e91 q^{76} -5.31820e90 q^{77} +8.46583e90 q^{78} +4.78463e91 q^{79} -6.94814e91 q^{80} +1.27316e92 q^{81} +6.01553e91 q^{82} -4.25318e89 q^{83} -8.44050e92 q^{84} -2.27773e93 q^{85} -1.90534e94 q^{86} -3.04747e93 q^{87} +1.07784e93 q^{88} +5.83257e94 q^{89} +2.85544e94 q^{90} +1.49366e94 q^{91} +1.47721e95 q^{92} -2.64643e95 q^{93} +6.15189e95 q^{94} +2.14601e95 q^{95} -9.60008e95 q^{96} +6.44354e95 q^{97} +2.72291e96 q^{98} +1.12440e96 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 16697241085008 q^{2} + 10\!\cdots\!96 q^{3}+ \cdots + 34\!\cdots\!51 q^{9}+O(q^{10}) $ 7 * q - 16697241085008 * q^2 + 100515854497394358147996 * q^3 + 163057083940695061811962902784 * q^4 - 3658387999529088680958306590731350 * q^5 - 30592714388364079315260992082788233536 * q^6 - 184642311743115370607493500489904481438408 * q^7 + 36028528195426625427479134330455698506199040 * q^8 + 34775775472129528349857305774273773877811641051 * q^9	$ 7 q - 16697241085008 q^{2} + 10\!\cdots\!96 q^{3}+ \cdots - 13\!\cdots\!28 q^{99}+O(q^{100}) $ 7 * q - 16697241085008 * q^2 + 100515854497394358147996 * q^3 + 163057083940695061811962902784 * q^4 - 3658387999529088680958306590731350 * q^5 - 30592714388364079315260992082788233536 * q^6 - 184642311743115370607493500489904481438408 * q^7 + 36028528195426625427479134330455698506199040 * q^8 + 34775775472129528349857305774273773877811641051 * q^9 + 2369114123959441270700616822719459966510786272800 * q^10 - 211379321299339211995860033669883746379479318698796 * q^11 + 29500590587146562092031430274877546417191966208812032 * q^12 - 883667637845783834437332163606692334928033653755299614 * q^13 + 24884922778173528138085777326574033504771595080747613568 * q^14 - 1421739776861319561135033238174867421082029896683725376600 * q^15 - 31468671341370205538262999960370611414173356196203424841728 * q^16 + 163250436637003263661570089512096377905088225334685131721342 * q^17 - 7054606772048003028382413409749231596837718873737440667537424 * q^18 + 133084372359310898958448501523235681541051727436663191570359820 * q^19 - 1318696260534044061297364386263469065025874939722479973417331200 * q^20 - 8226961344750528298533572507576209983448935264598913374247505696 * q^21 - 193421584410477868290586506488587370358898549812529751083484246976 * q^22 + 925260914184001305416523826357059292226482310773339215111132964776 * q^23 + 1719359518493251306391725804700467921422689016189510541760687554560 * q^24 - 15111829774373494694703308579556617230149980669179989285410298974375 * q^25 + 252570839996871764139482603418038366978372757286009959646749464447904 * q^26 - 16291464003153760806194022590188439733978909915063668620863256233960 * q^27 + 2270023864280230580582797832096861251181573169347509612847861972977664 * q^28 - 119228645746988213289933973286594685848645193803889692652451844737975470 * q^29 + 350448354156350400480979435069989695492221249186335731168327070817564800 * q^30 + 1783283666881858864849681148885200501497581294973934227348751364131906784 * q^31 - 5665372498136527985720301619489703024215195383428523596691479514791804928 * q^32 + 31524650657546522511070078635079454480923539002999356172307109465073458512 * q^33 - 360491523041063125717708388027762293189396999595568175085448186659598970272 * q^34 + 1278268341035082746531666145800358760269267683649420892787253371588938750800 * q^35 - 216561481226385812264597126278375191173372906326221899147967914271513631488 * q^36 - 4532061622841943284542390241171859851726205146853788500539269747469617514358 * q^37 - 2979582210919721773595405461863152858097797783237497905501709239616681227840 * q^38 + 43268347489134056222423767530379619668087154910038087692852374564634305176712 * q^39 - 252514831298472678734291758335102132215188475493571956673272319739362987008000 * q^40 + 123663386655433999860484853403953500874113711440208020678841289201379470695974 * q^41 + 3296122851141924824443574220618174749418258893075867148421980920155200276985344 * q^42 - 6595249409358954185694714287710218939626711013706300289026511229489118746183244 * q^43 + 31427981619155317050453798326367420934595218826815326227502736274099059309390848 * q^44 - 252057107931731391251960224707597558538839631727412739243273361199825466582835550 * q^45 + 333743461536679365083903174537100831945624746347277312419032904840551699600111744 * q^46 + 1582413179705462665936960636748613012540566075462612818643843634715630112826042192 * q^47 - 5861556434117332280930374286873664455351210291383528056190272983552191849213722624 * q^48 + 4345635008055985505106601346877321132027699788278385269907095782368403364891488399 * q^49 - 26742593205970009143775889336520990050133941492259748319418427757724876722706030000 * q^50 + 7043565089506559965061572069632281800522096763383079376468682406398600422146676984 * q^51 + 45800222007571685487736059984048709986270205428489770979037497696929384027946163712 * q^52 - 653999931744204429821742741003701830521617657540517458768483866216741544701292475654 * q^53 - 1692275654206728716605786947196644220317392594111136065941704729626944069981837438080 * q^54 - 2797264930804680667438884831689324464716285797264284803651188210713133784740241832200 * q^55 - 13571511538900847480549793700693331801076437559096966169392506220987757777557857402880 * q^56 - 32156245276763940566100505959698139630384956043693169857398532690693294678041975751120 * q^57 - 110275012470967940484400158535846043036245771061355495516009955997986614502808104491360 * q^58 - 289716843512018767811919727809674339112407721830489506743846640027004030301179845118940 * q^59 - 910863091257112962110410128770927709732237428874631129572443550789630933691032398899200 * q^60 - 1779644273771380099149369471014727845406783738447834645166296866716596067825339549188046 * q^61 - 4893410323209515393605311670149478112622973098189152140516775294151722525768562137565696 * q^62 - 12773855755538157144284595252262546905649007916763284311597736303148976241726684562602024 * q^63 - 24329532034212074257236420324752039539459926287390018025638252399891746834835822530789376 * q^64 - 40979880706222898178317998710539228015340375450212825952623031288613904725454054500850100 * q^65 - 142841613731497146561089386918878946227924637814625892149907766833242924230825872606056192 * q^66 - 183094181851902905703789039636502649221241410347877100016575616698548103898875205122783908 * q^67 - 250132580738896836682574414547500843555901286243235420681429272583107380144497499057716736 * q^68 - 372244836961332226973480986215431578494847115740354696097669790201492502675456308855459168 * q^69 - 587389541033882485666068522391834191601610745639266949076956170254929472707526921059782400 * q^70 - 36618527208607574135274147674246343687098099724640001025727994874106062220116534447931656 * q^71 + 2495502705800463241319297965149724088435827677064467496346161624547668625438549984339128320 * q^72 + 5937141741627411574629383951784847225959103237898806939243808260531064318159784943464907526 * q^73 + 25603418812897773069861990064614106209712057876935905208225093500026599325689360114519970848 * q^74 + 43416229043729585532262686371625117245611844558141193068941674421259839404159894884059222500 * q^75 + 64491781461168277038374423376126180174707623388661413952117963143585395013082375272839869440 * q^76 + 122801524700573133455664123216977109508839271312008866744292206338517188364407357732160152224 * q^77 + 256518622739178273010532892375526005382856863147760611859324715551823107217212845963281985152 * q^78 + 155279975164311735091235448536513906273532801204307686975280157544842456609207922540776901680 * q^79 + 343037548751841740038666995050634479050946344382038763901789904170114217394648666813900390400 * q^80 - 799336653019442009471583631583081099983526554777301855450568718504605547656753900698628831153 * q^81 - 2054599455199243418451530458808296516745297582440826399667363552358055209069956455679452833056 * q^82 - 2745080838526935126539434486643898932954125805020264508203796620734019354440308801326974021684 * q^83 - 12055830667015300843296227009204563031159870111997209215974794552386444770918151507927520305152 * q^84 - 16156906986132970771716277890961343081101351325821342812927748903601690598916612215092853170700 * q^85 - 16073101085057033129856695763368798351047883803740227513388827997968391823543719379002604387776 * q^86 - 44931373084677669249994770736329381356923858000626008622029156778901658182110994195783000791480 * q^87 - 20900444501134905678673788524771632932447417317035512416151379720801969394444956958395302789120 * q^88 + 8652425236627243255051028260917634407304730072980172181544783646255542601500269383337979350390 * q^89 + 169914380219009102880054256907856294069041898142575788262717672760376053145875718225670932330400 * q^90 + 235279610532724372901602846332263408075886672274330172793822218199845308058643167074949650230544 * q^91 + 622950794384614085632156625042963081233986358617743991991586248417198315809579918444522808891392 * q^92 + 1619655729334717431421579797164299646702152339363664709672746834797775058100318492643375449441152 * q^93 + 1784387548746436753701888750274366538460858609156963702431495773056050960861585984793528939671808 * q^94 + 1109691419127482658877926123378178695834970817464791602098716148821958373905367930889408748989000 * q^95 + 2773817117979873680694700349927475687549477810523157816910439588411515192104026991177258420404224 * q^96 - 462826972284038426621245345324758076530452205891330025493894671876723283114629445572915788984658 * q^97 - 10100804559243313775965110405631054964918520327952856127425837778067309219959758215138751854831056 * q^98 - 13792894935722775136702660269810636953813664741795563019740674282913700184659028566406972539495228 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−5.83847e14	−1.46671	−0.733355	−	0.679845i	$-0.762047\pi$
$2$	−5.83847e14	−1.46671	−0.733355	+	0.679845i	$0.762047\pi$
$3$	−6.70202e22	−0.485093	−0.242546	−	0.970140i	$-0.577983\pi$
$3$	−6.70202e22	−0.485093	−0.242546	+	0.970140i	$0.577983\pi$
$4$	1.82421e29	1.15124
$5$	3.35065e33	0.421778	0.210889	−	0.977510i	$-0.432364\pi$
$5$	3.35065e33	0.421778	0.210889	+	0.977510i	$0.432364\pi$
$6$	3.91296e37	0.711491
$7$	6.90378e40	0.710939	0.355469	−	0.934688i	$-0.384321\pi$
$7$	6.90378e40	0.710939	0.355469	+	0.934688i	$0.384321\pi$
$8$	−1.39919e43	−0.221826
$9$	−1.45964e46	−0.764685
$10$	−1.95627e48	−0.618627
$11$	−7.70331e49	−0.239404	−0.119702	−	0.992810i	$-0.538194\pi$
$11$	−7.70331e49	−0.239404	−0.119702	+	0.992810i	$0.538194\pi$
$12$	−1.22259e52	−0.558458
$13$	2.16354e53	0.203663	0.101831	−	0.994802i	$-0.467530\pi$
$13$	2.16354e53	0.203663	0.101831	+	0.994802i	$0.467530\pi$
$14$	−4.03075e55	−1.04274
$15$	−2.24561e56	−0.204602
$16$	−2.07367e58	−0.825886
$17$	−6.79786e59	−1.43087	−0.715434	−	0.698680i	$-0.753771\pi$
$17$	−6.79786e59	−1.43087	−0.715434	+	0.698680i	$0.753771\pi$
$18$	8.52204e60	1.12157
$19$	6.40476e61	0.612285	0.306142	−	0.951986i	$-0.400962\pi$
$19$	6.40476e61	0.612285	0.306142	+	0.951986i	$0.400962\pi$
$20$	6.11230e62	0.485568
$21$	−4.62693e63	−0.344871
$22$	4.49756e64	0.351137
$23$	8.09777e65	0.732091	0.366046	−	0.930597i	$-0.380711\pi$
$23$	8.09777e65	0.732091	0.366046	+	0.930597i	$0.380711\pi$
$24$	9.37741e65	0.107606
$25$	−5.18820e67	−0.822103
$26$	−1.26318e68	−0.298715
$27$	2.25754e69	0.856036
$28$	1.25940e70	0.818461
$29$	4.54709e70	0.538804	0.269402	−	0.963028i	$-0.413174\pi$
$29$	4.54709e70	0.538804	0.269402	+	0.963028i	$0.413174\pi$
$30$	1.31110e71	0.300091
$31$	3.94871e72	1.84252	0.921262	−	0.388943i	$-0.127160\pi$
$31$	3.94871e72	1.84252	0.921262	+	0.388943i	$0.127160\pi$
$32$	1.43242e73	1.43316
$33$	5.16277e72	0.116133
$34$	3.96891e74	2.09867
$35$	2.31322e74	0.299858
$36$	−2.66269e75	−0.880336
$37$	−1.34752e76	−1.17964	−0.589821	−	0.807534i	$-0.700802\pi$
$37$	−1.34752e76	−1.17964	−0.589821	+	0.807534i	$0.700802\pi$
$38$	−3.73940e76	−0.898044
$39$	−1.45001e76	−0.0987954
$40$	−4.68820e76	−0.0935614
$41$	−1.03033e77	−0.0620808	−0.0310404	−	0.999518i	$-0.509882\pi$
$41$	−1.03033e77	−0.0620808	−0.0310404	+	0.999518i	$0.509882\pi$
$42$	2.70142e78	0.505826
$43$	3.26343e79	1.95188	0.975942	−	0.218029i	$-0.0699628\pi$
$43$	3.26343e79	1.95188	0.975942	+	0.218029i	$0.0699628\pi$
$44$	−1.40525e79	−0.275612
$45$	−4.89073e79	−0.322527
$46$	−4.72786e80	−1.07377
$47$	−1.05368e81	−0.843263	−0.421632	−	0.906767i	$-0.638542\pi$
$47$	−1.05368e81	−0.843263	−0.421632	+	0.906767i	$0.638542\pi$
$48$	1.38978e81	0.400631
$49$	−4.66374e81	−0.494566
$50$	3.02912e82	1.20579
$51$	4.55594e82	0.694104
$52$	3.94675e82	0.234465
$53$	−3.91708e83	−0.923809	−0.461905	−	0.886930i	$-0.652834\pi$
$53$	−3.91708e83	−0.923809	−0.461905	+	0.886930i	$0.652834\pi$
$54$	−1.31806e84	−1.25556
$55$	−2.58111e83	−0.100976
$56$	−9.65971e83	−0.157705
$57$	−4.29248e84	−0.297015
$58$	−2.65481e85	−0.790269
$59$	8.07111e85	1.04860	0.524301	−	0.851533i	$-0.324327\pi$
$59$	8.07111e85	1.04860	0.524301	+	0.851533i	$0.324327\pi$
$60$	−4.09648e85	−0.235546
$61$	−4.86128e86	−1.25387	−0.626937	−	0.779070i	$-0.715692\pi$
$61$	−4.86128e86	−1.25387	−0.626937	+	0.779070i	$0.715692\pi$
$62$	−2.30544e87	−2.70245
$63$	−1.00770e87	−0.543644
$64$	−5.07726e87	−1.27615
$65$	7.24926e86	0.0859006
$66$	−3.01427e87	−0.170334
$67$	−6.80563e87	−0.185456	−0.0927280	−	0.995691i	$-0.529559\pi$
$67$	−6.80563e87	−0.185456	−0.0927280	+	0.995691i	$0.529559\pi$
$68$	−1.24008e89	−1.64727
$69$	−5.42714e88	−0.355132
$70$	−1.35057e89	−0.439806
$71$	−4.42259e89	−0.723847	−0.361924	−	0.932208i	$-0.617880\pi$
$71$	−4.42259e89	−0.723847	−0.361924	+	0.932208i	$0.617880\pi$
$72$	2.04231e89	0.169627
$73$	2.87024e90	1.22112	0.610561	−	0.791970i	$-0.290944\pi$
$73$	2.87024e90	1.22112	0.610561	+	0.791970i	$0.290944\pi$
$74$	7.86743e90	1.73019
$75$	3.47714e90	0.398796
$76$	1.16837e91	0.704887
$77$	−5.31820e90	−0.170202
$78$	8.46583e90	0.144904
$79$	4.78463e91	0.441503	0.220752	−	0.975330i	$-0.429149\pi$
$79$	4.78463e91	0.441503	0.220752	+	0.975330i	$0.429149\pi$
$80$	−6.94814e91	−0.348341
$81$	1.27316e92	0.349428
$82$	6.01553e91	0.0910546
$83$	−4.25318e89	−0.000357624 0	−0.000178812	−	1.00000i	$-0.500057\pi$
$83$	−4.25318e89	−0.000357624 0	−0.000178812		1.00000i	$0.500057\pi$
$84$	−8.44050e92	−0.397030
$85$	−2.27773e93	−0.603509
$86$	−1.90534e94	−2.86285
$87$	−3.04747e93	−0.261370
$88$	1.07784e93	0.0531062
$89$	5.83257e94	1.66129	0.830643	−	0.556805i	$-0.187973\pi$
$89$	5.83257e94	1.66129	0.830643	+	0.556805i	$0.187973\pi$
$90$	2.85544e94	0.473055
$91$	1.49366e94	0.144792
$92$	1.47721e95	0.842813
$93$	−2.64643e95	−0.893795
$94$	6.15189e95	1.23682
$95$	2.14601e95	0.258248
$96$	−9.60008e95	−0.695216
$97$	6.44354e95	0.282290	0.141145	−	0.989989i	$-0.454922\pi$
$97$	6.44354e95	0.282290	0.141145	+	0.989989i	$0.454922\pi$
$98$	2.72291e96	0.725386
$99$	1.12440e96	0.183069
$100$	−9.46438e96	−0.946438
$101$	−9.74501e96	−0.601445	−0.300722	−	0.953712i	$-0.597228\pi$
$101$	−9.74501e96	−0.601445	−0.300722	+	0.953712i	$0.597228\pi$
$102$	−2.65997e97	−1.01805
$103$	−4.41301e97	−1.05227	−0.526137	−	0.850400i	$-0.676360\pi$
$103$	−4.41301e97	−1.05227	−0.526137	+	0.850400i	$0.676360\pi$
$104$	−3.02720e96	−0.0451778
$105$	−1.55032e97	−0.145459
$106$	2.28697e98	1.35496
$107$	1.99620e98	0.750049	0.375025	−	0.927015i	$-0.377634\pi$
$107$	1.99620e98	0.750049	0.375025	+	0.927015i	$0.377634\pi$
$108$	4.11823e98	0.985503
$109$	−1.03070e98	−0.157742	−0.0788709	−	0.996885i	$-0.525131\pi$
$109$	−1.03070e98	−0.157742	−0.0788709	+	0.996885i	$0.525131\pi$
$110$	1.50698e98	0.148102
$111$	9.03107e98	0.572236
$112$	−1.43161e99	−0.587154
$113$	−4.58839e99	−1.22280	−0.611401	−	0.791321i	$-0.709394\pi$
$113$	−4.58839e99	−1.22280	−0.611401	+	0.791321i	$0.709394\pi$
$114$	2.50615e99	0.435635
$115$	2.71328e99	0.308780
$116$	8.29486e99	0.620293
$117$	−3.15798e99	−0.155738
$118$	−4.71230e100	−1.53800
$119$	−4.69310e100	−1.01726
$120$	3.14204e99	0.0453860
$121$	−9.76017e100	−0.942686
$122$	2.83825e101	1.83907
$123$	6.90526e99	0.0301150
$124$	7.20329e101	2.12119
$125$	−3.85294e101	−0.768523
$126$	5.88343e101	0.797369
$127$	−1.99520e101	−0.184291	−0.0921457	−	0.995746i	$-0.529373\pi$
$127$	−1.99520e101	−0.184291	−0.0921457	+	0.995746i	$0.529373\pi$
$128$	6.94593e101	0.438578
$129$	−2.18716e102	−0.946845
$130$	−4.23246e101	−0.125991
$131$	−9.51508e102	−1.95323	−0.976617	−	0.214985i	$-0.931030\pi$
$131$	−9.51508e102	−1.95323	−0.976617	+	0.214985i	$0.931030\pi$
$132$	9.41800e101	0.133697
$133$	4.42171e102	0.435297
$134$	3.97345e102	0.272010
$135$	7.56421e102	0.361057
$136$	9.51151e102	0.317404
$137$	−6.74942e103	−1.57877	−0.789386	−	0.613898i	$-0.789601\pi$
$137$	−6.74942e103	−1.57877	−0.789386	+	0.613898i	$0.789601\pi$
$138$	3.16862e103	0.520876
$139$	2.30236e103	0.266658	0.133329	−	0.991072i	$-0.457433\pi$
$139$	2.30236e103	0.266658	0.133329	+	0.991072i	$0.457433\pi$
$140$	4.21980e103	0.345209
$141$	7.06179e103	0.409061
$142$	2.58212e104	1.06167
$143$	−1.66664e103	−0.0487578
$144$	3.02680e104	0.631542
$145$	1.52357e104	0.227256
$146$	−1.67578e105	−1.79103
$147$	3.12565e104	0.239911
$148$	−2.45816e105	−1.35805
$149$	−2.93341e105	−1.16906	−0.584532	−	0.811370i	$-0.698722\pi$
$149$	−2.93341e105	−1.16906	−0.584532	+	0.811370i	$0.698722\pi$
$150$	−2.03012e105	−0.584919
$151$	8.38177e105	1.74966	0.874830	−	0.484430i	$-0.160973\pi$
$151$	8.38177e105	1.74966	0.874830	+	0.484430i	$0.160973\pi$
$152$	−8.96149e104	−0.135821
$153$	9.92240e105	1.09416
$154$	3.10502e105	0.249637
$155$	1.32308e106	0.777136
$156$	−2.64512e105	−0.113737
$157$	−1.89618e106	−0.598062	−0.299031	−	0.954243i	$-0.596663\pi$
$157$	−1.89618e106	−0.598062	−0.299031	+	0.954243i	$0.596663\pi$
$158$	−2.79349e106	−0.647558
$159$	2.62523e106	0.448133
$160$	4.79953e106	0.604476
$161$	5.59052e106	0.520472
$162$	−7.43329e106	−0.512510
$163$	−2.30939e107	−1.18141	−0.590703	−	0.806889i	$-0.701149\pi$
$163$	−2.30939e107	−1.18141	−0.590703	+	0.806889i	$0.701149\pi$
$164$	−1.87953e106	−0.0714700
$165$	1.72987e106	0.0489825
$166$	2.48321e104	0.000524530 0
$167$	−3.66382e107	−0.578343	−0.289172	−	0.957277i	$-0.593380\pi$
$167$	−3.66382e107	−0.578343	−0.289172	+	0.957277i	$0.593380\pi$
$168$	6.47396e106	0.0765014
$169$	−1.08170e108	−0.958521
$170$	1.32985e108	0.885173
$171$	−9.34862e107	−0.468205
$172$	5.95319e108	2.24709
$173$	3.43075e108	0.977583	0.488792	−	0.872401i	$-0.337438\pi$
$173$	3.43075e108	0.977583	0.488792	+	0.872401i	$0.337438\pi$
$174$	1.77926e108	0.383354
$175$	−3.58182e108	−0.584465
$176$	1.59741e108	0.197721
$177$	−5.40927e108	−0.508669
$178$	−3.40533e109	−2.43663
$179$	1.30322e108	0.0710632	0.0355316	−	0.999369i	$-0.488688\pi$
$179$	1.30322e108	0.0710632	0.0355316	+	0.999369i	$0.488688\pi$
$180$	−8.92174e108	−0.371307
$181$	2.41156e109	0.767163	0.383581	−	0.923507i	$-0.374691\pi$
$181$	2.41156e109	0.767163	0.383581	+	0.923507i	$0.374691\pi$
$182$	−8.72069e108	−0.212368
$183$	3.25804e109	0.608245
$184$	−1.13303e109	−0.162397
$185$	−4.51506e109	−0.497547
$186$	1.54511e110	1.31094
$187$	5.23661e109	0.342556
$188$	−1.92214e110	−0.970799
$189$	1.55855e110	0.608589
$190$	−1.25294e110	−0.378776
$191$	−3.22152e109	−0.0754992	−0.0377496	−	0.999287i	$-0.512019\pi$
$191$	−3.22152e109	−0.0754992	−0.0377496	+	0.999287i	$0.512019\pi$
$192$	3.40279e110	0.619050
$193$	8.70408e110	1.23082	0.615408	−	0.788209i	$-0.288991\pi$
$193$	8.70408e110	1.23082	0.615408	+	0.788209i	$0.288991\pi$
$194$	−3.76205e110	−0.414038
$195$	−4.85847e109	−0.0416697
$196$	−8.50766e110	−0.569365
$197$	−2.70756e111	−1.41568	−0.707842	−	0.706370i	$-0.750331\pi$
$197$	−2.70756e111	−1.41568	−0.707842	+	0.706370i	$0.750331\pi$
$198$	−6.56479e110	−0.268509
$199$	−3.05159e111	−0.977580	−0.488790	−	0.872402i	$-0.662562\pi$
$199$	−3.05159e111	−0.977580	−0.488790	+	0.872402i	$0.662562\pi$
$200$	7.25929e110	0.182364
$201$	4.56115e110	0.0899633
$202$	5.68960e111	0.882145
$203$	3.13921e111	0.383056
$204$	8.31101e111	0.799081
$205$	−3.45226e110	−0.0261843
$206$	2.57652e112	1.54338
$207$	−1.18198e112	−0.559819
$208$	−4.48646e111	−0.168202
$209$	−4.93379e111	−0.146584
$210$	9.05151e111	0.213346
$211$	−5.77934e112	−1.08188	−0.540940	−	0.841061i	$-0.681932\pi$
$211$	−5.77934e112	−1.08188	−0.540940	+	0.841061i	$0.681932\pi$
$212$	−7.14558e112	−1.06353
$213$	2.96403e112	0.351133
$214$	−1.16547e113	−1.10011
$215$	1.09346e113	0.823262
$216$	−3.15872e112	−0.189891
$217$	2.72610e113	1.30992
$218$	6.01771e112	0.231362
$219$	−1.92364e113	−0.592357
$220$	−4.70850e112	−0.116247
$221$	−1.47074e113	−0.291415
$222$	−5.27277e113	−0.839304
$223$	3.88674e113	0.497508	0.248754	−	0.968567i	$-0.419979\pi$
$223$	3.88674e113	0.497508	0.248754	+	0.968567i	$0.419979\pi$
$224$	9.88909e113	1.01889
$225$	7.57288e113	0.628650
$226$	2.67892e114	1.79350
$227$	−1.70800e114	−0.923067	−0.461534	−	0.887123i	$-0.652701\pi$
$227$	−1.70800e114	−0.923067	−0.461534	+	0.887123i	$0.652701\pi$
$228$	−7.83041e113	−0.341935
$229$	−2.73350e114	−0.965379	−0.482690	−	0.875792i	$-0.660340\pi$
$229$	−2.73350e114	−0.965379	−0.482690	+	0.875792i	$0.660340\pi$
$230$	−1.58414e114	−0.452891
$231$	3.56427e113	0.0825637
$232$	−6.36225e113	−0.119521
$233$	−1.28532e115	−1.95996	−0.979981	−	0.199090i	$-0.936201\pi$
$233$	−1.28532e115	−1.95996	−0.979981	+	0.199090i	$0.936201\pi$
$234$	1.84378e114	0.228423
$235$	−3.53052e114	−0.355670
$236$	1.47234e115	1.20719
$237$	−3.20667e114	−0.214170
$238$	2.74005e115	1.49203
$239$	1.25087e115	0.555793	0.277896	−	0.960611i	$-0.410363\pi$
$239$	1.25087e115	0.555793	0.277896	+	0.960611i	$0.410363\pi$
$240$	4.65665e114	0.168977
$241$	1.80824e114	0.0536327	0.0268164	−	0.999640i	$-0.491463\pi$
$241$	1.80824e114	0.0536327	0.0268164	+	0.999640i	$0.491463\pi$
$242$	5.69845e115	1.38265
$243$	−5.16247e115	−1.02554
$244$	−8.86802e115	−1.44351
$245$	−1.56266e115	−0.208597
$246$	−4.03162e114	−0.0441699
$247$	1.38569e115	0.124700
$248$	−5.52500e115	−0.408720
$249$	2.85049e112	0.000173481 0
$250$	2.24953e116	1.12720
$251$	−2.03012e116	−0.838195	−0.419098	−	0.907941i	$-0.637654\pi$
$251$	−2.03012e116	−0.838195	−0.419098	+	0.907941i	$0.637654\pi$
$252$	−1.83826e116	−0.625865
$253$	−6.23796e115	−0.175266
$254$	1.16489e116	0.270302
$255$	1.52654e116	0.292758
$256$	3.98988e116	0.632880
$257$	−6.80143e116	−0.892985	−0.446492	−	0.894787i	$-0.647327\pi$
$257$	−6.80143e116	−0.892985	−0.446492	+	0.894787i	$0.647327\pi$
$258$	1.27697e117	1.38875
$259$	−9.30295e116	−0.838653
$260$	1.32242e116	0.0988922
$261$	−6.63709e116	−0.412015
$262$	5.55535e117	2.86483
$263$	−1.45139e117	−0.622200	−0.311100	−	0.950377i	$-0.600697\pi$
$263$	−1.45139e117	−0.622200	−0.311100	+	0.950377i	$0.600697\pi$
$264$	−7.22371e115	−0.0257614
$265$	−1.31248e117	−0.389643
$266$	−2.58160e117	−0.638454
$267$	−3.90900e117	−0.805878
$268$	−1.24149e117	−0.213504
$269$	−1.14539e118	−1.64425	−0.822124	−	0.569308i	$-0.807211\pi$
$269$	−1.14539e118	−1.64425	−0.822124	+	0.569308i	$0.807211\pi$
$270$	−4.41635e117	−0.529567
$271$	−6.19618e116	−0.0621032	−0.0310516	−	0.999518i	$-0.509886\pi$
$271$	−6.19618e116	−0.0621032	−0.0310516	+	0.999518i	$0.509886\pi$
$272$	1.40965e118	1.18173
$273$	−1.00105e117	−0.0702374
$274$	3.94063e118	2.31560
$275$	3.99663e117	0.196815
$276$	−9.90026e117	−0.408843
$277$	4.27618e118	1.48179	0.740896	−	0.671620i	$-0.234401\pi$
$277$	4.27618e118	1.48179	0.740896	+	0.671620i	$0.234401\pi$
$278$	−1.34423e118	−0.391111
$279$	−5.76368e118	−1.40895
$280$	−3.23663e117	−0.0665164
$281$	7.51875e117	0.129984	0.0649919	−	0.997886i	$-0.479298\pi$
$281$	7.51875e117	0.129984	0.0649919	+	0.997886i	$0.479298\pi$
$282$	−4.12301e118	−0.599974
$283$	7.76285e118	0.951435	0.475718	−	0.879598i	$-0.342188\pi$
$283$	7.76285e118	0.951435	0.475718	+	0.879598i	$0.342188\pi$
$284$	−8.06775e118	−0.833322
$285$	−1.43826e118	−0.125274
$286$	9.73064e117	0.0715136
$287$	−7.11314e117	−0.0441357
$288$	−2.09080e119	−1.09592
$289$	2.36402e119	1.04738
$290$	−8.89533e118	−0.333318
$291$	−4.31848e118	−0.136937
$292$	5.23592e119	1.40580
$293$	−6.26805e119	−1.42578	−0.712891	−	0.701275i	$-0.752615\pi$
$293$	−6.26805e119	−1.42578	−0.712891	+	0.701275i	$0.752615\pi$
$294$	−1.82490e119	−0.351879
$295$	2.70435e119	0.442277
$296$	1.88543e119	0.261675
$297$	−1.73905e119	−0.204939
$298$	1.71266e120	1.71468
$299$	1.75198e119	0.149100
$300$	6.34305e119	0.459110
$301$	2.25300e120	1.38767
$302$	−4.89367e120	−2.56625
$303$	6.53112e119	0.291756
$304$	−1.32813e120	−0.505677
$305$	−1.62885e120	−0.528857
$306$	−5.79317e120	−1.60482
$307$	2.36229e120	0.558627	0.279313	−	0.960200i	$-0.409893\pi$
$307$	2.36229e120	0.558627	0.279313	+	0.960200i	$0.409893\pi$
$308$	−9.70153e119	−0.195943
$309$	2.95760e120	0.510451
$310$	−7.72474e120	−1.13983
$311$	5.28228e120	0.666719	0.333359	−	0.942800i	$-0.391818\pi$
$311$	5.28228e120	0.666719	0.333359	+	0.942800i	$0.391818\pi$
$312$	2.02884e119	0.0219154
$313$	1.82170e121	1.68491	0.842455	−	0.538767i	$-0.181110\pi$
$313$	1.82170e121	1.68491	0.842455	+	0.538767i	$0.181110\pi$
$314$	1.10708e121	0.877183
$315$	−3.37645e120	−0.229297
$316$	8.72818e120	0.508277
$317$	8.99213e120	0.449250	0.224625	−	0.974445i	$-0.427884\pi$
$317$	8.99213e120	0.449250	0.224625	+	0.974445i	$0.427884\pi$
$318$	−1.53273e121	−0.657282
$319$	−3.50276e120	−0.128992
$320$	−1.70121e121	−0.538251
$321$	−1.33785e121	−0.363844
$322$	−3.26401e121	−0.763382
$323$	−4.35387e121	−0.876099
$324$	2.32251e121	0.402276
$325$	−1.12249e121	−0.167432
$326$	1.34833e122	1.73278
$327$	6.90776e120	0.0765194
$328$	1.44162e120	0.0137712
$329$	−7.27438e121	−0.599508
$330$	−1.00998e121	−0.0718432
$331$	−3.04250e122	−1.86884	−0.934421	−	0.356170i	$-0.884082\pi$
$331$	−3.04250e122	−1.86884	−0.934421	+	0.356170i	$0.884082\pi$
$332$	−7.75870e118	−0.000411711 0
$333$	1.96688e122	0.902055
$334$	2.13911e122	0.848262
$335$	−2.28033e121	−0.0782213
$336$	9.59471e121	0.284824
$337$	2.30471e121	0.0592333	0.0296166	−	0.999561i	$-0.490571\pi$
$337$	2.30471e121	0.0592333	0.0296166	+	0.999561i	$0.490571\pi$
$338$	6.31548e122	1.40587
$339$	3.07515e122	0.593172
$340$	−4.15506e122	−0.694784
$341$	−3.04181e122	−0.441108
$342$	5.45816e122	0.686721
$343$	−9.72998e122	−1.06254
$344$	−4.56616e122	−0.432979
$345$	−1.81845e122	−0.149787
$346$	−2.00304e123	−1.43383
$347$	4.50560e122	0.280397	0.140198	−	0.990123i	$-0.455226\pi$
$347$	4.50560e122	0.280397	0.140198	+	0.990123i	$0.455226\pi$
$348$	−5.55923e122	−0.300899
$349$	−1.53732e123	−0.723985	−0.361993	−	0.932181i	$-0.617903\pi$
$349$	−1.53732e123	−0.723985	−0.361993	+	0.932181i	$0.617903\pi$
$350$	2.09124e123	0.857241
$351$	4.88426e122	0.174343
$352$	−1.10343e123	−0.343105
$353$	4.15794e123	1.12669	0.563346	−	0.826221i	$-0.309514\pi$
$353$	4.15794e123	1.12669	0.563346	+	0.826221i	$0.309514\pi$
$354$	3.15819e123	0.746071
$355$	−1.48186e123	−0.305303
$356$	1.06399e124	1.91254
$357$	3.14532e123	0.493465
$358$	−7.60880e122	−0.104229
$359$	−1.43762e124	−1.72014	−0.860071	−	0.510174i	$-0.829581\pi$
$359$	−1.43762e124	−1.72014	−0.860071	+	0.510174i	$0.829581\pi$
$360$	6.84307e122	0.0715450
$361$	−6.83997e123	−0.625108
$362$	−1.40798e124	−1.12521
$363$	6.54128e123	0.457290
$364$	2.72475e123	0.166690
$365$	9.61716e123	0.515042
$366$	−1.90220e124	−0.892120
$367$	1.83642e124	0.754516	0.377258	−	0.926108i	$-0.376867\pi$
$367$	1.83642e124	0.754516	0.377258	+	0.926108i	$0.376867\pi$
$368$	−1.67921e124	−0.604624
$369$	1.50390e123	0.0474723
$370$	2.63610e124	0.729758
$371$	−2.70426e124	−0.656772
$372$	−4.82766e124	−1.02897
$373$	7.96172e124	1.48980	0.744901	−	0.667175i	$-0.232497\pi$
$373$	7.96172e124	1.48980	0.744901	+	0.667175i	$0.232497\pi$
$374$	−3.05738e124	−0.502431
$375$	2.58225e124	0.372805
$376$	1.47430e124	0.187058
$377$	9.83780e123	0.109734
$378$	−9.09957e124	−0.892624
$379$	1.19379e125	1.03021	0.515105	−	0.857127i	$-0.327753\pi$
$379$	1.19379e125	1.03021	0.515105	+	0.857127i	$0.327753\pi$
$380$	3.91479e124	0.297306
$381$	1.33718e124	0.0893984
$382$	1.88088e124	0.110736
$383$	3.37136e125	1.74850	0.874248	−	0.485479i	$-0.161355\pi$
$383$	3.37136e125	1.74850	0.874248	+	0.485479i	$0.161355\pi$
$384$	−4.65518e124	−0.212751
$385$	−1.78194e124	−0.0717874
$386$	−5.08185e125	−1.80525
$387$	−4.76342e125	−1.49258
$388$	1.17544e125	0.324984
$389$	−4.69324e125	−1.14529	−0.572647	−	0.819802i	$-0.694084\pi$
$389$	−4.69324e125	−1.14529	−0.572647	+	0.819802i	$0.694084\pi$
$390$	2.83660e124	0.0611175
$391$	−5.50475e125	−1.04753
$392$	6.52547e124	0.109708
$393$	6.37702e125	0.947500
$394$	1.58080e126	2.07640
$395$	1.60316e125	0.186217
$396$	2.05115e125	0.210756
$397$	−5.04903e125	−0.459059	−0.229529	−	0.973302i	$-0.573719\pi$
$397$	−5.04903e125	−0.459059	−0.229529	+	0.973302i	$0.573719\pi$
$398$	1.78166e126	1.43383
$399$	−2.96344e125	−0.211159
$400$	1.07586e126	0.678963
$401$	−2.67177e126	−1.49382	−0.746908	−	0.664928i	$-0.768462\pi$
$401$	−2.67177e126	−1.49382	−0.746908	+	0.664928i	$0.768462\pi$
$402$	−2.66301e125	−0.131950
$403$	8.54318e125	0.375254
$404$	−1.77770e126	−0.692407
$405$	4.26590e125	0.147381
$406$	−1.83282e126	−0.561833
$407$	1.03803e126	0.282412
$408$	−6.37463e125	−0.153970
$409$	−4.90786e126	−1.05272	−0.526358	−	0.850263i	$-0.676443\pi$
$409$	−4.90786e126	−1.05272	−0.526358	+	0.850263i	$0.676443\pi$
$410$	2.01559e125	0.0384049
$411$	4.52348e126	0.765850
$412$	−8.05027e126	−1.21142
$413$	5.57212e126	0.745492
$414$	6.90095e126	0.821093
$415$	−1.42509e123	−0.000150838 0
$416$	3.09909e126	0.291882
$417$	−1.54304e126	−0.129354
$418$	2.88058e126	0.214996
$419$	−1.02929e127	−0.684161	−0.342080	−	0.939671i	$-0.611132\pi$
$419$	−1.02929e127	−0.684161	−0.342080	+	0.939671i	$0.611132\pi$
$420$	−2.82812e126	−0.167458
$421$	−2.08808e127	−1.10171	−0.550853	−	0.834602i	$-0.685698\pi$
$421$	−2.08808e127	−1.10171	−0.550853	+	0.834602i	$0.685698\pi$
$422$	3.37425e127	1.58681
$423$	1.53799e127	0.644831
$424$	5.48074e126	0.204925
$425$	3.52687e127	1.17632
$426$	−1.73054e127	−0.515010
$427$	−3.35612e127	−0.891428
$428$	3.64149e127	0.863487
$429$	1.11699e126	0.0236521
$430$	−6.38415e127	−1.20749
$431$	−1.23952e127	−0.209462	−0.104731	−	0.994501i	$-0.533398\pi$
$431$	−1.23952e127	−0.209462	−0.104731	+	0.994501i	$0.533398\pi$
$432$	−4.68138e127	−0.706988
$433$	1.56574e127	0.211377	0.105688	−	0.994399i	$-0.466295\pi$
$433$	1.56574e127	0.211377	0.105688	+	0.994399i	$0.466295\pi$
$434$	−1.59163e128	−1.92128
$435$	−1.02110e127	−0.110240
$436$	−1.88022e127	−0.181599
$437$	5.18643e127	0.448248
$438$	1.12311e128	0.868816
$439$	2.13684e128	1.47993	0.739966	−	0.672644i	$-0.234842\pi$
$439$	2.13684e128	1.47993	0.739966	+	0.672644i	$0.234842\pi$
$440$	3.61147e126	0.0223990
$441$	6.80736e127	0.378188
$442$	8.58690e127	0.427421
$443$	−4.20970e127	−0.187789	−0.0938945	−	0.995582i	$-0.529932\pi$
$443$	−4.20970e127	−0.187789	−0.0938945	+	0.995582i	$0.529932\pi$
$444$	1.64746e128	0.658781
$445$	1.95429e128	0.700695
$446$	−2.26926e128	−0.729700
$447$	1.96598e128	0.567105
$448$	−3.50523e128	−0.907263
$449$	−1.69559e128	−0.393889	−0.196944	−	0.980415i	$-0.563102\pi$
$449$	−1.69559e128	−0.393889	−0.196944	+	0.980415i	$0.563102\pi$
$450$	−4.42141e128	−0.922048
$451$	7.93692e126	0.0148624
$452$	−8.37021e128	−1.40774
$453$	−5.61748e128	−0.848747
$454$	9.97210e128	1.35387
$455$	5.00473e127	0.0610700
$456$	6.00601e127	0.0658857
$457$	6.71852e128	0.662732	0.331366	−	0.943502i	$-0.392490\pi$
$457$	6.71852e128	0.662732	0.331366	+	0.943502i	$0.392490\pi$
$458$	1.59595e129	1.41593
$459$	−1.53464e129	−1.22487
$460$	4.94960e128	0.355480
$461$	1.27947e128	0.0827059	0.0413530	−	0.999145i	$-0.486833\pi$
$461$	1.27947e128	0.0827059	0.0413530	+	0.999145i	$0.486833\pi$
$462$	−2.08099e128	−0.121097
$463$	−2.36080e129	−1.23703	−0.618517	−	0.785772i	$-0.712266\pi$
$463$	−2.36080e129	−1.23703	−0.618517	+	0.785772i	$0.712266\pi$
$464$	−9.42915e128	−0.444990
$465$	−8.86728e128	−0.376983
$466$	7.50428e129	2.87470
$467$	−2.49064e128	−0.0859890	−0.0429945	−	0.999075i	$-0.513690\pi$
$467$	−2.49064e128	−0.0859890	−0.0429945	+	0.999075i	$0.513690\pi$
$468$	−5.76082e128	−0.179292
$469$	−4.69846e128	−0.131848
$470$	2.06128e129	0.521665
$471$	1.27082e129	0.290115
$472$	−1.12930e129	−0.232607
$473$	−2.51392e129	−0.467290
$474$	1.87220e129	0.314126
$475$	−3.32292e129	−0.503361
$476$	−8.56121e129	−1.17111
$477$	5.71750e129	0.706423
$478$	−7.30315e129	−0.815187
$479$	1.88392e129	0.190016	0.0950079	−	0.995477i	$-0.469712\pi$
$479$	1.88392e129	0.190016	0.0950079	+	0.995477i	$0.469712\pi$
$480$	−3.21665e129	−0.293227
$481$	−2.91540e129	−0.240249
$482$	−1.05574e129	−0.0786637
$483$	−3.74678e129	−0.252477
$484$	−1.78046e130	−1.08526
$485$	2.15901e129	0.119064
$486$	3.01409e130	1.50417
$487$	2.37286e130	1.07181	0.535905	−	0.844278i	$-0.319970\pi$
$487$	2.37286e130	1.07181	0.535905	+	0.844278i	$0.319970\pi$
$488$	6.80187e129	0.278142
$489$	1.54776e130	0.573091
$490$	9.12353e129	0.305952
$491$	4.05512e130	1.23183	0.615916	−	0.787812i	$-0.288786\pi$
$491$	4.05512e130	1.23183	0.615916	+	0.787812i	$0.288786\pi$
$492$	1.25967e129	0.0346696
$493$	−3.09105e130	−0.770957
$494$	−8.09034e129	−0.182898
$495$	3.76748e129	0.0772145
$496$	−8.18831e130	−1.52171
$497$	−3.05326e130	−0.514611
$498$	−1.66425e127	−0.000254446 0
$499$	−9.81259e130	−1.36115	−0.680577	−	0.732677i	$-0.738271\pi$
$499$	−9.81259e130	−1.36115	−0.680577	+	0.732677i	$0.738271\pi$
$500$	−7.02859e130	−0.884755
$501$	2.45550e130	0.280550
$502$	1.18528e131	1.22939
$503$	6.79384e130	0.639835	0.319918	−	0.947445i	$-0.396345\pi$
$503$	6.79384e130	0.639835	0.319918	+	0.947445i	$0.396345\pi$
$504$	1.40997e130	0.120594
$505$	−3.26521e130	−0.253676
$506$	3.64202e130	0.257064
$507$	7.24958e130	0.464972
$508$	−3.63966e130	−0.212164
$509$	5.69322e130	0.301679	0.150840	−	0.988558i	$-0.451802\pi$
$509$	5.69322e130	0.301679	0.150840	+	0.988558i	$0.451802\pi$
$510$	−8.91265e130	−0.429391
$511$	1.98155e131	0.868142
$512$	−3.43011e131	−1.36683
$513$	1.44590e131	0.524138
$514$	3.97100e131	1.30975
$515$	−1.47864e131	−0.443827
$516$	−3.98984e131	−1.09005
$517$	8.11683e130	0.201881
$518$	5.43150e131	1.23006
$519$	−2.29930e131	−0.474218
$520$	−1.01431e130	−0.0190550
$521$	−3.68378e131	−0.630470	−0.315235	−	0.949014i	$-0.602083\pi$
$521$	−3.68378e131	−0.630470	−0.315235	+	0.949014i	$0.602083\pi$
$522$	3.87505e131	0.604307
$523$	1.18924e132	1.69019	0.845097	−	0.534612i	$-0.179542\pi$
$523$	1.18924e132	1.69019	0.845097	+	0.534612i	$0.179542\pi$
$524$	−1.73575e132	−2.24864
$525$	2.40054e131	0.283520
$526$	8.47389e131	0.912587
$527$	−2.68428e132	−2.63641
$528$	−1.07059e131	−0.0959129
$529$	−5.67751e131	−0.464042
$530$	7.66286e131	0.571493
$531$	−1.17809e132	−0.801850
$532$	8.06614e131	0.501131
$533$	−2.22915e130	−0.0126436
$534$	2.28226e132	1.18199
$535$	6.68856e131	0.316355
$536$	9.52238e130	0.0411390
$537$	−8.73418e130	−0.0344722
$538$	6.68732e132	2.41164
$539$	3.59263e131	0.118401
$540$	1.37987e132	0.415664
$541$	−2.36643e132	−0.651667	−0.325834	−	0.945427i	$-0.605645\pi$
$541$	−2.36643e132	−0.651667	−0.325834	+	0.945427i	$0.605645\pi$
$542$	3.61763e131	0.0910874
$543$	−1.61623e132	−0.372145
$544$	−9.73737e132	−2.05067
$545$	−3.45351e131	−0.0665320
$546$	5.84462e131	0.103018
$547$	1.92705e132	0.310819	0.155410	−	0.987850i	$-0.450330\pi$
$547$	1.92705e132	0.310819	0.155410	+	0.987850i	$0.450330\pi$
$548$	−1.23124e133	−1.81755
$549$	7.09570e132	0.958819
$550$	−2.33342e132	−0.288671
$551$	2.91230e132	0.329901
$552$	7.59361e131	0.0787776
$553$	3.30320e132	0.313882
$554$	−2.49664e133	−2.17336
$555$	3.02600e132	0.241357
$556$	4.19999e132	0.306988
$557$	1.79501e133	1.20251	0.601256	−	0.799056i	$-0.294667\pi$
$557$	1.79501e133	1.20251	0.601256	+	0.799056i	$0.294667\pi$
$558$	3.36511e133	2.06652
$559$	7.06055e132	0.397526
$560$	−4.79684e132	−0.247649
$561$	−3.50958e132	−0.166172
$562$	−4.38980e132	−0.190649
$563$	−1.01835e133	−0.405734	−0.202867	−	0.979206i	$-0.565026\pi$
$563$	−1.01835e133	−0.405734	−0.202867	+	0.979206i	$0.565026\pi$
$564$	1.28822e133	0.470927
$565$	−1.53741e133	−0.515751
$566$	−4.53232e133	−1.39548
$567$	8.78959e132	0.248422
$568$	6.18805e132	0.160568
$569$	−2.33472e132	−0.0556275	−0.0278137	−	0.999613i	$-0.508855\pi$
$569$	−2.33472e132	−0.0556275	−0.0278137	+	0.999613i	$0.508855\pi$
$570$	8.39725e132	0.183741
$571$	5.08228e133	1.02143	0.510713	−	0.859751i	$-0.329381\pi$
$571$	5.08228e133	1.02143	0.510713	+	0.859751i	$0.329381\pi$
$572$	−3.04031e132	−0.0561320
$573$	2.15907e132	0.0366241
$574$	4.15299e132	0.0647343
$575$	−4.20128e133	−0.601855
$576$	7.41095e133	0.975851
$577$	−8.84079e133	−1.07020	−0.535099	−	0.844790i	$-0.679726\pi$
$577$	−8.84079e133	−1.07020	−0.535099	+	0.844790i	$0.679726\pi$
$578$	−1.38023e134	−1.53621
$579$	−5.83349e133	−0.597060
$580$	2.77932e133	0.261626
$581$	−2.93630e130	−0.000254248 0
$582$	2.52133e133	0.200847
$583$	3.01745e133	0.221164
$584$	−4.01601e133	−0.270877
$585$	−1.05813e133	−0.0656869
$586$	3.65959e134	2.09121
$587$	2.22867e132	0.0117246	0.00586230	−	0.999983i	$-0.498134\pi$
$587$	2.22867e132	0.0117246	0.00586230	+	0.999983i	$0.498134\pi$
$588$	5.70185e133	0.276195
$589$	2.52906e134	1.12815
$590$	−1.57893e134	−0.648693
$591$	1.81461e134	0.686738
$592$	2.79430e134	0.974249
$593$	−4.55149e134	−1.46218	−0.731091	−	0.682280i	$-0.760989\pi$
$593$	−4.55149e134	−1.46218	−0.731091	+	0.682280i	$0.760989\pi$
$594$	1.01534e134	0.300586
$595$	−1.57249e134	−0.429058
$596$	−5.35116e134	−1.34587
$597$	2.04518e134	0.474217
$598$	−1.02289e134	−0.218686
$599$	−6.27199e134	−1.23653	−0.618265	−	0.785970i	$-0.712164\pi$
$599$	−6.27199e134	−1.23653	−0.618265	+	0.785970i	$0.712164\pi$
$600$	−4.86519e133	−0.0884634
$601$	4.81009e133	0.0806754	0.0403377	−	0.999186i	$-0.487157\pi$
$601$	4.81009e133	0.0806754	0.0403377	+	0.999186i	$0.487157\pi$
$602$	−1.31541e135	−2.03531
$603$	9.93374e133	0.141815
$604$	1.52901e135	2.01428
$605$	−3.27029e134	−0.397604
$606$	−3.81318e134	−0.427922
$607$	1.10577e135	1.14554	0.572772	−	0.819715i	$-0.305868\pi$
$607$	1.10577e135	1.14554	0.572772	+	0.819715i	$0.305868\pi$
$608$	9.17428e134	0.877503
$609$	−2.10390e134	−0.185818
$610$	9.50998e134	0.775680
$611$	−2.27968e134	−0.171741
$612$	1.81006e135	1.25965
$613$	−5.32449e134	−0.342330	−0.171165	−	0.985242i	$-0.554753\pi$
$613$	−5.32449e134	−0.342330	−0.171165	+	0.985242i	$0.554753\pi$
$614$	−1.37922e135	−0.819344
$615$	2.31371e133	0.0127018
$616$	7.44118e133	0.0377552
$617$	−4.56704e134	−0.214193	−0.107096	−	0.994249i	$-0.534155\pi$
$617$	−4.56704e134	−0.214193	−0.107096	+	0.994249i	$0.534155\pi$
$618$	−1.72679e135	−0.748684
$619$	−2.05911e135	−0.825434	−0.412717	−	0.910859i	$-0.635420\pi$
$619$	−2.05911e135	−0.825434	−0.412717	+	0.910859i	$0.635420\pi$
$620$	2.41357e135	0.894671
$621$	1.82810e135	0.626696
$622$	−3.08405e135	−0.977884
$623$	4.02668e135	1.18107
$624$	3.00683e134	0.0815937
$625$	1.98323e135	0.497957
$626$	−1.06360e136	−2.47128
$627$	3.30663e134	0.0711067
$628$	−3.45903e135	−0.688513
$629$	9.16023e135	1.68791
$630$	1.97133e135	0.336313
$631$	−7.07385e135	−1.11746	−0.558730	−	0.829350i	$-0.688711\pi$
$631$	−7.07385e135	−1.11746	−0.558730	+	0.829350i	$0.688711\pi$
$632$	−6.69461e134	−0.0979370
$633$	3.87333e135	0.524813
$634$	−5.25003e135	−0.658920
$635$	−6.68521e134	−0.0777301
$636$	4.78898e135	0.515909
$637$	−1.00902e135	−0.100725
$638$	2.04508e135	0.189194
$639$	6.45537e135	0.553515
$640$	2.32734e135	0.184983
$641$	−5.92561e135	−0.436635	−0.218317	−	0.975878i	$-0.570057\pi$
$641$	−5.92561e135	−0.436635	−0.218317	+	0.975878i	$0.570057\pi$
$642$	7.81102e135	0.533653
$643$	1.09509e136	0.693775	0.346888	−	0.937907i	$-0.387238\pi$
$643$	1.09509e136	0.693775	0.346888	+	0.937907i	$0.387238\pi$
$644$	1.01983e136	0.599188
$645$	−7.32840e135	−0.399359
$646$	2.54199e136	1.28498
$647$	−1.50172e136	−0.704259	−0.352130	−	0.935951i	$-0.614542\pi$
$647$	−1.50172e136	−0.704259	−0.352130	+	0.935951i	$0.614542\pi$
$648$	−1.78139e135	−0.0775123
$649$	−6.21743e135	−0.251040
$650$	6.55361e135	0.245574
$651$	−1.82704e136	−0.635433
$652$	−4.21283e136	−1.36008
$653$	−5.06181e136	−1.51711	−0.758554	−	0.651610i	$-0.774094\pi$
$653$	−5.06181e136	−1.51711	−0.758554	+	0.651610i	$0.774094\pi$
$654$	−4.03308e135	−0.112232
$655$	−3.18817e136	−0.823832
$656$	2.13655e135	0.0512717
$657$	−4.18950e136	−0.933773
$658$	4.24713e136	0.879305
$659$	6.39975e136	1.23089	0.615447	−	0.788178i	$-0.288976\pi$
$659$	6.39975e136	1.23089	0.615447	+	0.788178i	$0.288976\pi$
$660$	3.15564e135	0.0563907
$661$	3.20255e136	0.531771	0.265886	−	0.964005i	$-0.414336\pi$
$661$	3.20255e136	0.531771	0.265886	+	0.964005i	$0.414336\pi$
$662$	1.77635e137	2.74105
$663$	9.85695e135	0.141363
$664$	5.95101e132	7.93303e−5 0
$665$	1.48156e136	0.183599
$666$	−1.14836e137	−1.32305
$667$	3.68213e136	0.394453
$668$	−6.68360e136	−0.665812
$669$	−2.60490e136	−0.241337
$670$	1.33137e136	0.114728
$671$	3.74480e136	0.300183
$672$	−6.62768e136	−0.494256
$673$	1.36574e137	0.947624	0.473812	−	0.880626i	$-0.342878\pi$
$673$	1.36574e137	0.947624	0.473812	+	0.880626i	$0.342878\pi$
$674$	−1.34560e136	−0.0868781
$675$	−1.17125e137	−0.703750
$676$	−1.97325e137	−1.10349
$677$	6.34558e136	0.330309	0.165155	−	0.986268i	$-0.447188\pi$
$677$	6.34558e136	0.330309	0.165155	+	0.986268i	$0.447188\pi$
$678$	−1.79542e137	−0.870012
$679$	4.44848e136	0.200691
$680$	3.18698e136	0.133874
$681$	1.14470e137	0.447773
$682$	1.77596e137	0.646979
$683$	−6.97947e136	−0.236820	−0.118410	−	0.992965i	$-0.537780\pi$
$683$	−6.97947e136	−0.236820	−0.118410	+	0.992965i	$0.537780\pi$
$684$	−1.70539e137	−0.539016
$685$	−2.26150e137	−0.665891
$686$	5.68082e137	1.55845
$687$	1.83200e137	0.468298
$688$	−6.76727e137	−1.61203
$689$	−8.47474e136	−0.188146
$690$	1.06169e137	0.219694
$691$	−1.23454e137	−0.238132	−0.119066	−	0.992886i	$-0.537990\pi$
$691$	−1.23454e137	−0.238132	−0.119066	+	0.992886i	$0.537990\pi$
$692$	6.25843e137	1.12543
$693$	7.76263e136	0.130151
$694$	−2.63058e137	−0.411261
$695$	7.71440e136	0.112471
$696$	4.26399e136	0.0579786
$697$	7.00401e136	0.0888295
$698$	8.97557e137	1.06188
$699$	8.61421e137	0.950763
$700$	−6.53400e137	−0.672860
$701$	6.92489e137	0.665410	0.332705	−	0.943031i	$-0.392039\pi$
$701$	6.92489e137	0.665410	0.332705	+	0.943031i	$0.392039\pi$
$702$	−2.85166e137	−0.255710
$703$	−8.63052e137	−0.722277
$704$	3.91117e137	0.305516
$705$	2.36616e137	0.172533
$706$	−2.42760e138	−1.65253
$707$	−6.72774e137	−0.427590
$708$	−9.86767e137	−0.585601
$709$	−1.70945e138	−0.947358	−0.473679	−	0.880698i	$-0.657074\pi$
$709$	−1.70945e138	−0.947358	−0.473679	+	0.880698i	$0.657074\pi$
$710$	8.65178e137	0.447791
$711$	−6.98381e137	−0.337611
$712$	−8.16088e137	−0.368517
$713$	3.19757e138	1.34890
$714$	−1.83639e138	−0.723771
$715$	−5.58433e136	−0.0205650
$716$	2.37735e137	0.0818108
$717$	−8.38333e137	−0.269611
$718$	8.39353e138	2.52295
$719$	1.48193e138	0.416367	0.208184	−	0.978090i	$-0.433245\pi$
$719$	1.48193e138	0.416367	0.208184	+	0.978090i	$0.433245\pi$
$720$	1.01417e138	0.266371
$721$	−3.04664e138	−0.748103
$722$	3.99350e138	0.916852
$723$	−1.21189e137	−0.0260169
$724$	4.39920e138	0.883189
$725$	−2.35912e138	−0.442952
$726$	−3.81911e138	−0.670712
$727$	3.25371e138	0.534515	0.267257	−	0.963625i	$-0.413883\pi$
$727$	3.25371e138	0.534515	0.267257	+	0.963625i	$0.413883\pi$
$728$	−2.08991e137	−0.0321186
$729$	1.02969e138	0.148054
$730$	−5.61495e138	−0.755418
$731$	−2.21843e139	−2.79289
$732$	5.94336e138	0.700237
$733$	−2.16095e138	−0.238288	−0.119144	−	0.992877i	$-0.538015\pi$
$733$	−2.16095e138	−0.238288	−0.119144	+	0.992877i	$0.538015\pi$
$734$	−1.07219e139	−1.10666
$735$	1.04730e138	0.101189
$736$	1.15994e139	1.04921
$737$	5.24259e137	0.0443990
$738$	−8.78048e137	−0.0696281
$739$	1.66699e139	1.23788	0.618938	−	0.785440i	$-0.287563\pi$
$739$	1.66699e139	1.23788	0.618938	+	0.785440i	$0.287563\pi$
$740$	−8.23643e138	−0.572797
$741$	−9.28695e137	−0.0604909
$742$	1.57888e139	0.963294
$743$	1.75642e139	1.00386	0.501928	−	0.864909i	$-0.332624\pi$
$743$	1.75642e139	1.00386	0.501928	+	0.864909i	$0.332624\pi$
$744$	3.70287e138	0.198267
$745$	−9.82883e138	−0.493086
$746$	−4.64843e139	−2.18511
$747$	6.20809e135	0.000273469 0
$748$	9.55269e138	0.394365
$749$	1.37813e139	0.533239
$750$	−1.50764e139	−0.546797
$751$	−1.73208e138	−0.0588886	−0.0294443	−	0.999566i	$-0.509374\pi$
$751$	−1.73208e138	−0.0588886	−0.0294443	+	0.999566i	$0.509374\pi$
$752$	2.18498e139	0.696439
$753$	1.36059e139	0.406603
$754$	−5.74377e138	−0.160948
$755$	2.80844e139	0.737968
$756$	2.84313e139	0.700632
$757$	5.71470e139	1.32082	0.660409	−	0.750906i	$-0.270383\pi$
$757$	5.71470e139	1.32082	0.660409	+	0.750906i	$0.270383\pi$
$758$	−6.96990e139	−1.51102
$759$	4.18069e138	0.0850202
$760$	−3.00268e138	−0.0572862
$761$	−6.07920e139	−1.08816	−0.544078	−	0.839035i	$-0.683120\pi$
$761$	−6.07920e139	−1.08816	−0.544078	+	0.839035i	$0.683120\pi$
$762$	−7.80711e138	−0.131122
$763$	−7.11572e138	−0.112145
$764$	−5.87674e138	−0.0869178
$765$	3.32465e139	0.461494
$766$	−1.96836e140	−2.56454
$767$	1.74622e139	0.213561
$768$	−2.67403e139	−0.307006
$769$	1.78977e139	0.192916	0.0964581	−	0.995337i	$-0.469249\pi$
$769$	1.78977e139	0.192916	0.0964581	+	0.995337i	$0.469249\pi$
$770$	1.04038e139	0.105291
$771$	4.55833e139	0.433180
$772$	1.58781e140	1.41697
$773$	−2.05403e140	−1.72147	−0.860737	−	0.509050i	$-0.829997\pi$
$773$	−2.05403e140	−1.72147	−0.860737	+	0.509050i	$0.829997\pi$
$774$	2.78111e140	2.18918
$775$	−2.04867e140	−1.51474
$776$	−9.01575e138	−0.0626193
$777$	6.23486e139	0.406824
$778$	2.74014e140	1.67982
$779$	−6.59899e138	−0.0380111
$780$	−8.86288e138	−0.0479719
$781$	3.40686e139	0.173292
$782$	3.21393e140	1.53642
$783$	1.02652e140	0.461235
$784$	9.67105e139	0.408455
$785$	−6.35343e139	−0.252249
$786$	−3.72321e140	−1.38971
$787$	−3.06281e140	−1.07485	−0.537423	−	0.843313i	$-0.680602\pi$
$787$	−3.06281e140	−1.07485	−0.537423	+	0.843313i	$0.680602\pi$
$788$	−4.93917e140	−1.62979
$789$	9.72723e139	0.301825
$790$	−9.36002e139	−0.273126
$791$	−3.16773e140	−0.869337
$792$	−1.57325e139	−0.0406095
$793$	−1.05176e140	−0.255368
$794$	2.94786e140	0.673307
$795$	8.79624e139	0.189013
$796$	−5.56675e140	−1.12543
$797$	8.29211e140	1.57738	0.788690	−	0.614791i	$-0.210760\pi$
$797$	8.29211e140	1.57738	0.788690	+	0.614791i	$0.210760\pi$
$798$	1.73019e140	0.309710
$799$	7.16278e140	1.20660
$800$	−7.43166e140	−1.17821
$801$	−8.51342e140	−1.27036
$802$	1.55991e141	2.19100
$803$	−2.21103e140	−0.292342
$804$	8.32051e139	0.103569
$805$	1.87319e140	0.219524
$806$	−4.98792e140	−0.550389
$807$	7.67642e140	0.797613
$808$	1.36351e140	0.133416
$809$	4.87641e140	0.449363	0.224681	−	0.974432i	$-0.427866\pi$
$809$	4.87641e140	0.449363	0.224681	+	0.974432i	$0.427866\pi$
$810$	−2.49064e140	−0.216166
$811$	−1.48806e141	−1.21649	−0.608245	−	0.793749i	$-0.708126\pi$
$811$	−1.48806e141	−1.21649	−0.608245	+	0.793749i	$0.708126\pi$
$812$	5.72659e140	0.440990
$813$	4.15269e139	0.0301258
$814$	−6.06053e140	−0.414216
$815$	−7.73797e140	−0.498291
$816$	−9.44751e140	−0.573250
$817$	2.09015e141	1.19511
$818$	2.86544e141	1.54403
$819$	−2.18020e140	−0.110720
$820$	−6.29767e139	−0.0301445
$821$	−3.37463e141	−1.52259	−0.761296	−	0.648404i	$-0.775437\pi$
$821$	−3.37463e141	−1.52259	−0.761296	+	0.648404i	$0.775437\pi$
$822$	−2.64102e141	−1.12328
$823$	3.03955e141	1.21876	0.609379	−	0.792879i	$-0.291419\pi$
$823$	3.03955e141	1.21876	0.609379	+	0.792879i	$0.291419\pi$
$824$	6.17464e140	0.233422
$825$	−2.67855e140	−0.0954736
$826$	−3.25327e141	−1.09342
$827$	2.34651e141	0.743712	0.371856	−	0.928291i	$-0.378722\pi$
$827$	2.34651e141	0.743712	0.371856	+	0.928291i	$0.378722\pi$
$828$	−2.15618e141	−0.644487
$829$	−2.14659e141	−0.605138	−0.302569	−	0.953127i	$-0.597844\pi$
$829$	−2.14659e141	−0.605138	−0.302569	+	0.953127i	$0.597844\pi$
$830$	8.32036e137	0.000221235 0
$831$	−2.86590e141	−0.718807
$832$	−1.09849e141	−0.259904
$833$	3.17035e141	0.707659
$834$	9.00902e140	0.189725
$835$	−1.22762e141	−0.243933
$836$	−9.00028e140	−0.168753
$837$	8.91435e141	1.57727
$838$	6.00949e141	1.00347
$839$	1.17010e142	1.84404	0.922018	−	0.387147i	$-0.126539\pi$
$839$	1.17010e142	1.84404	0.922018	+	0.387147i	$0.126539\pi$
$840$	2.16920e140	0.0322666
$841$	−5.05446e141	−0.709691
$842$	1.21912e142	1.61588
$843$	−5.03908e140	−0.0630542
$844$	−1.05428e142	−1.24551
$845$	−3.62440e141	−0.404283
$846$	−8.97951e141	−0.945780
$847$	−6.73821e141	−0.670191
$848$	8.12271e141	0.762961
$849$	−5.20268e141	−0.461534
$850$	−2.05915e142	−1.72532
$851$	−1.09119e142	−0.863606
$852$	5.40702e141	0.404239
$853$	−1.42014e142	−1.00300	−0.501502	−	0.865156i	$-0.667219\pi$
$853$	−1.42014e142	−1.00300	−0.501502	+	0.865156i	$0.667219\pi$
$854$	1.95946e142	1.30747
$855$	−3.13240e141	−0.197479
$856$	−2.79306e141	−0.166381
$857$	1.75601e142	0.988457	0.494228	−	0.869332i	$-0.335451\pi$
$857$	1.75601e142	0.988457	0.494228	+	0.869332i	$0.335451\pi$
$858$	−6.52149e140	−0.0346907
$859$	−9.84281e141	−0.494824	−0.247412	−	0.968910i	$-0.579580\pi$
$859$	−9.84281e141	−0.494824	−0.247412	+	0.968910i	$0.579580\pi$
$860$	1.99471e142	0.947773
$861$	4.76724e140	0.0214099
$862$	7.23690e141	0.307220
$863$	−2.03809e142	−0.817898	−0.408949	−	0.912557i	$-0.634105\pi$
$863$	−2.03809e142	−0.817898	−0.408949	+	0.912557i	$0.634105\pi$
$864$	3.23373e142	1.22684
$865$	1.14953e142	0.412323
$866$	−9.14154e141	−0.310028
$867$	−1.58437e142	−0.508079
$868$	4.97299e142	1.50803
$869$	−3.68575e141	−0.105698
$870$	5.96167e141	0.161690
$871$	−1.47242e141	−0.0377705
$872$	1.44215e141	0.0349913
$873$	−9.40522e141	−0.215863
$874$	−3.02808e142	−0.657450
$875$	−2.65999e142	−0.546373
$876$	−3.50912e142	−0.681945
$877$	6.71671e142	1.23503	0.617513	−	0.786560i	$-0.288140\pi$
$877$	6.71671e142	1.23503	0.617513	+	0.786560i	$0.288140\pi$
$878$	−1.24759e143	−2.17063
$879$	4.20086e142	0.691636
$880$	5.35237e141	0.0833943
$881$	5.35745e142	0.790000	0.395000	−	0.918681i	$-0.370745\pi$
$881$	5.35745e142	0.790000	0.395000	+	0.918681i	$0.370745\pi$
$882$	−3.97446e142	−0.554692
$883$	5.85018e142	0.772815	0.386407	−	0.922328i	$-0.373716\pi$
$883$	5.85018e142	0.772815	0.386407	+	0.922328i	$0.373716\pi$
$884$	−2.68295e142	−0.335489
$885$	−1.81246e142	−0.214546
$886$	2.45782e142	0.275432
$887$	2.79695e142	0.296749	0.148375	−	0.988931i	$-0.452596\pi$
$887$	2.79695e142	0.296749	0.148375	+	0.988931i	$0.452596\pi$
$888$	−1.26362e142	−0.126937
$889$	−1.37744e142	−0.131020
$890$	−1.14101e143	−1.02772
$891$	−9.80751e141	−0.0836547
$892$	7.09024e142	0.572751
$893$	−6.74858e142	−0.516317
$894$	−1.14783e143	−0.831778
$895$	4.36663e141	0.0299729
$896$	4.79532e142	0.311802
$897$	−1.17418e142	−0.0723272
$898$	9.89966e142	0.577721
$899$	1.79551e143	0.992759
$900$	1.38145e143	0.723727
$901$	2.66278e143	1.32185
$902$	−4.63395e141	−0.0217989
$903$	−1.50996e143	−0.673149
$904$	6.42004e142	0.271250
$905$	8.08030e142	0.323572
$906$	3.27975e143	1.24487
$907$	−3.67331e143	−1.32161	−0.660806	−	0.750557i	$-0.729785\pi$
$907$	−3.67331e143	−1.32161	−0.660806	+	0.750557i	$0.729785\pi$
$908$	−3.11575e143	−1.06267
$909$	1.42242e143	0.459916
$910$	−2.92200e142	−0.0895721
$911$	−4.83487e143	−1.40522	−0.702609	−	0.711576i	$-0.747982\pi$
$911$	−4.83487e143	−1.40522	−0.702609	+	0.711576i	$0.747982\pi$
$912$	8.90118e142	0.245300
$913$	3.27636e139	8.56167e−5 0
$914$	−3.92259e143	−0.972037
$915$	1.09166e143	0.256545
$916$	−4.98648e143	−1.11138
$917$	−6.56900e143	−1.38863
$918$	8.95996e143	1.79654
$919$	−1.68259e143	−0.320020	−0.160010	−	0.987115i	$-0.551153\pi$
$919$	−1.68259e143	−0.320020	−0.160010	+	0.987115i	$0.551153\pi$
$920$	−3.79640e142	−0.0684955
$921$	−1.58321e143	−0.270986
$922$	−7.47018e142	−0.121306
$923$	−9.56844e142	−0.147421
$924$	6.50198e142	0.0950507
$925$	6.99118e143	0.969787
$926$	1.37835e144	1.81437
$927$	6.44138e143	0.804659
$928$	6.51332e143	0.772193
$929$	8.20174e143	0.922877	0.461438	−	0.887172i	$-0.347334\pi$
$929$	8.20174e143	0.922877	0.461438	+	0.887172i	$0.347334\pi$
$930$	5.17714e143	0.552925
$931$	−2.98702e143	−0.302815
$932$	−2.34469e144	−2.25639
$933$	−3.54020e143	−0.323420
$934$	1.45416e143	0.126121
$935$	1.75460e143	0.144483
$936$	4.41861e142	0.0345468
$937$	−1.99615e144	−1.48191	−0.740955	−	0.671554i	$-0.765627\pi$
$937$	−1.99615e144	−1.48191	−0.740955	+	0.671554i	$0.765627\pi$
$938$	2.74318e143	0.193383
$939$	−1.22091e144	−0.817338
$940$	−6.44042e143	−0.409462
$941$	3.14315e144	1.89788	0.948940	−	0.315457i	$-0.102158\pi$
$941$	3.14315e144	1.89788	0.948940	+	0.315457i	$0.102158\pi$
$942$	−7.41966e143	−0.425515
$943$	−8.34334e142	−0.0454488
$944$	−1.67368e144	−0.866025
$945$	5.22217e143	0.256690
$946$	1.46775e144	0.685379
$947$	−1.27087e144	−0.563801	−0.281900	−	0.959444i	$-0.590965\pi$
$947$	−1.27087e144	−0.563801	−0.281900	+	0.959444i	$0.590965\pi$
$948$	−5.84964e143	−0.246561
$949$	6.20986e143	0.248697
$950$	1.94008e144	0.738285
$951$	−6.02654e143	−0.217928
$952$	6.56654e143	0.225655
$953$	−9.96813e143	−0.325543	−0.162771	−	0.986664i	$-0.552043\pi$
$953$	−9.96813e143	−0.325543	−0.162771	+	0.986664i	$0.552043\pi$
$954$	−3.33815e144	−1.03612
$955$	−1.07942e143	−0.0318439
$956$	2.28185e144	0.639851
$957$	2.34756e143	0.0625731
$958$	−1.09992e144	−0.278698
$959$	−4.65965e144	−1.12241
$960$	1.14016e144	0.261102
$961$	1.09994e145	2.39489
$962$	1.70215e144	0.352376
$963$	−2.91372e144	−0.573552
$964$	3.29862e143	0.0617442
$965$	2.91643e144	0.519132
$966$	2.18755e144	0.370311
$967$	−5.05508e144	−0.813849	−0.406925	−	0.913462i	$-0.633399\pi$
$967$	−5.05508e144	−0.813849	−0.406925	+	0.913462i	$0.633399\pi$
$968$	1.36563e144	0.209112
$969$	2.91797e144	0.424989
$970$	−1.26053e144	−0.174632
$971$	6.88191e144	0.906935	0.453467	−	0.891273i	$-0.350187\pi$
$971$	6.88191e144	0.906935	0.453467	+	0.891273i	$0.350187\pi$
$972$	−9.41744e144	−1.18064
$973$	1.58950e144	0.189578
$974$	−1.38539e145	−1.57204
$975$	7.52293e143	0.0812200
$976$	1.00807e145	1.03556
$977$	7.10079e144	0.694097	0.347049	−	0.937847i	$-0.387184\pi$
$977$	7.10079e144	0.694097	0.347049	+	0.937847i	$0.387184\pi$
$978$	−9.03655e144	−0.840559
$979$	−4.49301e144	−0.397719
$980$	−2.85062e144	−0.240146
$981$	1.50444e144	0.120623
$982$	−2.36757e145	−1.80674
$983$	−1.55473e145	−1.12930	−0.564652	−	0.825329i	$-0.690989\pi$
$983$	−1.55473e145	−1.12930	−0.564652	+	0.825329i	$0.690989\pi$
$984$	−9.66178e142	−0.00668029
$985$	−9.07210e144	−0.597105
$986$	1.80470e145	1.13077
$987$	4.87531e144	0.290817
$988$	2.52780e144	0.143559
$989$	2.64265e145	1.42896
$990$	−2.19963e144	−0.113251
$991$	−1.31496e145	−0.644673	−0.322337	−	0.946625i	$-0.604468\pi$
$991$	−1.31496e145	−0.644673	−0.322337	+	0.946625i	$0.604468\pi$
$992$	5.65620e145	2.64063
$993$	2.03909e145	0.906562
$994$	1.78264e145	0.754785
$995$	−1.02248e145	−0.412322
$996$	5.19990e141	0.000199718 0
$997$	−4.24439e145	−1.55275	−0.776373	−	0.630274i	$-0.782943\pi$
$997$	−4.24439e145	−1.55275	−0.776373	+	0.630274i	$0.782943\pi$
$998$	5.72905e145	1.99642
$999$	−3.04206e145	−1.00982

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.98.a.a.1.1	✓	7
3.2	odd	2		9.98.a.a.1.7		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.98.a.a.1.1	✓	7	1.1	even	1	trivial
9.98.a.a.1.7		7	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1 \)
Weight:	\( k \)	\(=\)	\( 98 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)

\(f(q)\)	\(=\)	\(q-5.83847e14 q^{2} -6.70202e22 q^{3} +1.82421e29 q^{4} +3.35065e33 q^{5} +3.91296e37 q^{6} +6.90378e40 q^{7} -1.39919e43 q^{8} -1.45964e46 q^{9} +O(q^{10})\)	\(q-5.83847e14 q^{2} -6.70202e22 q^{3} +1.82421e29 q^{4} +3.35065e33 q^{5} +3.91296e37 q^{6} +6.90378e40 q^{7} -1.39919e43 q^{8} -1.45964e46 q^{9} -1.95627e48 q^{10} -7.70331e49 q^{11} -1.22259e52 q^{12} +2.16354e53 q^{13} -4.03075e55 q^{14} -2.24561e56 q^{15} -2.07367e58 q^{16} -6.79786e59 q^{17} +8.52204e60 q^{18} +6.40476e61 q^{19} +6.11230e62 q^{20} -4.62693e63 q^{21} +4.49756e64 q^{22} +8.09777e65 q^{23} +9.37741e65 q^{24} -5.18820e67 q^{25} -1.26318e68 q^{26} +2.25754e69 q^{27} +1.25940e70 q^{28} +4.54709e70 q^{29} +1.31110e71 q^{30} +3.94871e72 q^{31} +1.43242e73 q^{32} +5.16277e72 q^{33} +3.96891e74 q^{34} +2.31322e74 q^{35} -2.66269e75 q^{36} -1.34752e76 q^{37} -3.73940e76 q^{38} -1.45001e76 q^{39} -4.68820e76 q^{40} -1.03033e77 q^{41} +2.70142e78 q^{42} +3.26343e79 q^{43} -1.40525e79 q^{44} -4.89073e79 q^{45} -4.72786e80 q^{46} -1.05368e81 q^{47} +1.38978e81 q^{48} -4.66374e81 q^{49} +3.02912e82 q^{50} +4.55594e82 q^{51} +3.94675e82 q^{52} -3.91708e83 q^{53} -1.31806e84 q^{54} -2.58111e83 q^{55} -9.65971e83 q^{56} -4.29248e84 q^{57} -2.65481e85 q^{58} +8.07111e85 q^{59} -4.09648e85 q^{60} -4.86128e86 q^{61} -2.30544e87 q^{62} -1.00770e87 q^{63} -5.07726e87 q^{64} +7.24926e86 q^{65} -3.01427e87 q^{66} -6.80563e87 q^{67} -1.24008e89 q^{68} -5.42714e88 q^{69} -1.35057e89 q^{70} -4.42259e89 q^{71} +2.04231e89 q^{72} +2.87024e90 q^{73} +7.86743e90 q^{74} +3.47714e90 q^{75} +1.16837e91 q^{76} -5.31820e90 q^{77} +8.46583e90 q^{78} +4.78463e91 q^{79} -6.94814e91 q^{80} +1.27316e92 q^{81} +6.01553e91 q^{82} -4.25318e89 q^{83} -8.44050e92 q^{84} -2.27773e93 q^{85} -1.90534e94 q^{86} -3.04747e93 q^{87} +1.07784e93 q^{88} +5.83257e94 q^{89} +2.85544e94 q^{90} +1.49366e94 q^{91} +1.47721e95 q^{92} -2.64643e95 q^{93} +6.15189e95 q^{94} +2.14601e95 q^{95} -9.60008e95 q^{96} +6.44354e95 q^{97} +2.72291e96 q^{98} +1.12440e96 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 16697241085008 q^{2} + 10\!\cdots\!96 q^{3}+ \cdots + 34\!\cdots\!51 q^{9}+O(q^{10}) \) 7 * q - 16697241085008 * q^2 + 100515854497394358147996 * q^3 + 163057083940695061811962902784 * q^4 - 3658387999529088680958306590731350 * q^5 - 30592714388364079315260992082788233536 * q^6 - 184642311743115370607493500489904481438408 * q^7 + 36028528195426625427479134330455698506199040 * q^8 + 34775775472129528349857305774273773877811641051 * q^9	\( 7 q - 16697241085008 q^{2} + 10\!\cdots\!96 q^{3}+ \cdots - 13\!\cdots\!28 q^{99}+O(q^{100}) \) 7 * q - 16697241085008 * q^2 + 100515854497394358147996 * q^3 + 163057083940695061811962902784 * q^4 - 3658387999529088680958306590731350 * q^5 - 30592714388364079315260992082788233536 * q^6 - 184642311743115370607493500489904481438408 * q^7 + 36028528195426625427479134330455698506199040 * q^8 + 34775775472129528349857305774273773877811641051 * q^9 + 2369114123959441270700616822719459966510786272800 * q^10 - 211379321299339211995860033669883746379479318698796 * q^11 + 29500590587146562092031430274877546417191966208812032 * q^12 - 883667637845783834437332163606692334928033653755299614 * q^13 + 24884922778173528138085777326574033504771595080747613568 * q^14 - 1421739776861319561135033238174867421082029896683725376600 * q^15 - 31468671341370205538262999960370611414173356196203424841728 * q^16 + 163250436637003263661570089512096377905088225334685131721342 * q^17 - 7054606772048003028382413409749231596837718873737440667537424 * q^18 + 133084372359310898958448501523235681541051727436663191570359820 * q^19 - 1318696260534044061297364386263469065025874939722479973417331200 * q^20 - 8226961344750528298533572507576209983448935264598913374247505696 * q^21 - 193421584410477868290586506488587370358898549812529751083484246976 * q^22 + 925260914184001305416523826357059292226482310773339215111132964776 * q^23 + 1719359518493251306391725804700467921422689016189510541760687554560 * q^24 - 15111829774373494694703308579556617230149980669179989285410298974375 * q^25 + 252570839996871764139482603418038366978372757286009959646749464447904 * q^26 - 16291464003153760806194022590188439733978909915063668620863256233960 * q^27 + 2270023864280230580582797832096861251181573169347509612847861972977664 * q^28 - 119228645746988213289933973286594685848645193803889692652451844737975470 * q^29 + 350448354156350400480979435069989695492221249186335731168327070817564800 * q^30 + 1783283666881858864849681148885200501497581294973934227348751364131906784 * q^31 - 5665372498136527985720301619489703024215195383428523596691479514791804928 * q^32 + 31524650657546522511070078635079454480923539002999356172307109465073458512 * q^33 - 360491523041063125717708388027762293189396999595568175085448186659598970272 * q^34 + 1278268341035082746531666145800358760269267683649420892787253371588938750800 * q^35 - 216561481226385812264597126278375191173372906326221899147967914271513631488 * q^36 - 4532061622841943284542390241171859851726205146853788500539269747469617514358 * q^37 - 2979582210919721773595405461863152858097797783237497905501709239616681227840 * q^38 + 43268347489134056222423767530379619668087154910038087692852374564634305176712 * q^39 - 252514831298472678734291758335102132215188475493571956673272319739362987008000 * q^40 + 123663386655433999860484853403953500874113711440208020678841289201379470695974 * q^41 + 3296122851141924824443574220618174749418258893075867148421980920155200276985344 * q^42 - 6595249409358954185694714287710218939626711013706300289026511229489118746183244 * q^43 + 31427981619155317050453798326367420934595218826815326227502736274099059309390848 * q^44 - 252057107931731391251960224707597558538839631727412739243273361199825466582835550 * q^45 + 333743461536679365083903174537100831945624746347277312419032904840551699600111744 * q^46 + 1582413179705462665936960636748613012540566075462612818643843634715630112826042192 * q^47 - 5861556434117332280930374286873664455351210291383528056190272983552191849213722624 * q^48 + 4345635008055985505106601346877321132027699788278385269907095782368403364891488399 * q^49 - 26742593205970009143775889336520990050133941492259748319418427757724876722706030000 * q^50 + 7043565089506559965061572069632281800522096763383079376468682406398600422146676984 * q^51 + 45800222007571685487736059984048709986270205428489770979037497696929384027946163712 * q^52 - 653999931744204429821742741003701830521617657540517458768483866216741544701292475654 * q^53 - 1692275654206728716605786947196644220317392594111136065941704729626944069981837438080 * q^54 - 2797264930804680667438884831689324464716285797264284803651188210713133784740241832200 * q^55 - 13571511538900847480549793700693331801076437559096966169392506220987757777557857402880 * q^56 - 32156245276763940566100505959698139630384956043693169857398532690693294678041975751120 * q^57 - 110275012470967940484400158535846043036245771061355495516009955997986614502808104491360 * q^58 - 289716843512018767811919727809674339112407721830489506743846640027004030301179845118940 * q^59 - 910863091257112962110410128770927709732237428874631129572443550789630933691032398899200 * q^60 - 1779644273771380099149369471014727845406783738447834645166296866716596067825339549188046 * q^61 - 4893410323209515393605311670149478112622973098189152140516775294151722525768562137565696 * q^62 - 12773855755538157144284595252262546905649007916763284311597736303148976241726684562602024 * q^63 - 24329532034212074257236420324752039539459926287390018025638252399891746834835822530789376 * q^64 - 40979880706222898178317998710539228015340375450212825952623031288613904725454054500850100 * q^65 - 142841613731497146561089386918878946227924637814625892149907766833242924230825872606056192 * q^66 - 183094181851902905703789039636502649221241410347877100016575616698548103898875205122783908 * q^67 - 250132580738896836682574414547500843555901286243235420681429272583107380144497499057716736 * q^68 - 372244836961332226973480986215431578494847115740354696097669790201492502675456308855459168 * q^69 - 587389541033882485666068522391834191601610745639266949076956170254929472707526921059782400 * q^70 - 36618527208607574135274147674246343687098099724640001025727994874106062220116534447931656 * q^71 + 2495502705800463241319297965149724088435827677064467496346161624547668625438549984339128320 * q^72 + 5937141741627411574629383951784847225959103237898806939243808260531064318159784943464907526 * q^73 + 25603418812897773069861990064614106209712057876935905208225093500026599325689360114519970848 * q^74 + 43416229043729585532262686371625117245611844558141193068941674421259839404159894884059222500 * q^75 + 64491781461168277038374423376126180174707623388661413952117963143585395013082375272839869440 * q^76 + 122801524700573133455664123216977109508839271312008866744292206338517188364407357732160152224 * q^77 + 256518622739178273010532892375526005382856863147760611859324715551823107217212845963281985152 * q^78 + 155279975164311735091235448536513906273532801204307686975280157544842456609207922540776901680 * q^79 + 343037548751841740038666995050634479050946344382038763901789904170114217394648666813900390400 * q^80 - 799336653019442009471583631583081099983526554777301855450568718504605547656753900698628831153 * q^81 - 2054599455199243418451530458808296516745297582440826399667363552358055209069956455679452833056 * q^82 - 2745080838526935126539434486643898932954125805020264508203796620734019354440308801326974021684 * q^83 - 12055830667015300843296227009204563031159870111997209215974794552386444770918151507927520305152 * q^84 - 16156906986132970771716277890961343081101351325821342812927748903601690598916612215092853170700 * q^85 - 16073101085057033129856695763368798351047883803740227513388827997968391823543719379002604387776 * q^86 - 44931373084677669249994770736329381356923858000626008622029156778901658182110994195783000791480 * q^87 - 20900444501134905678673788524771632932447417317035512416151379720801969394444956958395302789120 * q^88 + 8652425236627243255051028260917634407304730072980172181544783646255542601500269383337979350390 * q^89 + 169914380219009102880054256907856294069041898142575788262717672760376053145875718225670932330400 * q^90 + 235279610532724372901602846332263408075886672274330172793822218199845308058643167074949650230544 * q^91 + 622950794384614085632156625042963081233986358617743991991586248417198315809579918444522808891392 * q^92 + 1619655729334717431421579797164299646702152339363664709672746834797775058100318492643375449441152 * q^93 + 1784387548746436753701888750274366538460858609156963702431495773056050960861585984793528939671808 * q^94 + 1109691419127482658877926123378178695834970817464791602098716148821958373905367930889408748989000 * q^95 + 2773817117979873680694700349927475687549477810523157816910439588411515192104026991177258420404224 * q^96 - 462826972284038426621245345324758076530452205891330025493894671876723283114629445572915788984658 * q^97 - 10100804559243313775965110405631054964918520327952856127425837778067309219959758215138751854831056 * q^98 - 13792894935722775136702660269810636953813664741795563019740674282913700184659028566406972539495228 * q^99

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